Tetsu Shimomura

Last Updated :2024/04/03

Affiliations, Positions
Graduate School of Humanities and Social Sciences, Professor
E-mail
tshimohiroshima-u.ac.jp

Basic Information

Academic Degrees

  • Doctor of Philosophy, Hiroshima University
  • Master, Hiroshima University

Research Fields

  • Mathematical and physical sciences;Mathematics;Basic analysis

Research Keywords

  • Sobolev functions

Educational Activity

Course in Charge

  1. 2024, Undergraduate Education, 1Term, Computer Practice
  2. 2024, Undergraduate Education, 2Term, Computer Practice
  3. 2024, Undergraduate Education, 2Term, Research Methods in Analysis I
  4. 2024, Undergraduate Education, 4Term, Study of Instructional Materials in Analysis
  5. 2024, Undergraduate Education, Second Semester, Graduation Thesis
  6. 2024, Undergraduate Education, First Semester, Study of Instructional Materials in Analysis Education
  7. 2024, Undergraduate Education, Second Semester, Practical Seminar for the Teaching Profession
  8. 2024, Graduate Education (Master's Program) , First Semester, Special Study in Mathematics Education A
  9. 2024, Graduate Education (Master's Program) , Second Semester, Special Study in Mathematics Education A
  10. 2024, Graduate Education (Master's Program) , 3Term, Basic Course in Teaching Material Design for Science and Culture (Mathematics) b
  11. 2024, Graduate Education (Doctoral Program) , First Semester, Special Study
  12. 2024, Graduate Education (Doctoral Program) , Second Semester, Special Study

Research Activities

Academic Papers

  1. Vanishing exponential integrability for Riesz potentials in Morrey-Orlicz spaces, MATHEMATISCHE NACHRICHTEN, 297(1), 110-125, 202401
  2. Sobolev type inequalities for fractional maximal functions and Riesz potentials in Morrey spaces of variable exponent on half spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 73(4), 1201-1217, 202312
  3. Integrability for Hardy operators of double phase, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 42(3-4), 375-402, 2023
  4. Generalized solution of the double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces, HIROSHIMA MATHEMATICAL JOURNAL, 53(3), 359-372, 202311
  5. Hardy-Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces, ACTA MATHEMATICA HUNGARICA, 171(2), 221-240, 202312
  6. Continuity of Generalized Riesz Potentials for Double Phase Functionals with Variable Exponents over Metric Measure Spaces, TAIWANESE JOURNAL OF MATHEMATICS, 27(4), 813-832, 202308
  7. VANISHING MORREY INTEGRABILITY FOR RIESZ POTENTIALS IN MORREY-ORLICZ SPACES, MATHEMATICA SCANDINAVICA, 129(2), 374-400, 2023
  8. Continuity of Riesz potentials for double phase functionals with variable exponents, PUBLICATIONES MATHEMATICAE DEBRECEN, 103(1-2), 171-186, 2023
  9. BOUNDEDNESS OF INTEGRAL OPERATORS OF DOUBLE PHASE, MATHEMATICAL INEQUALITIES & APPLICATIONS, 26(3), 703-716, 202307
  10. Trudinger's inequality for Riesz potentials on Musielak-Orlicz spaces over metric measure spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 68(10), 1694-1714, 20231003
  11. Sobolev's inequality in Musielak-Orlicz-Morrey spaces of an integral form, MATHEMATISCHE NACHRICHTEN, 296(9), 4152-4168, 202309
  12. Hardy-Sobolev inequalities for double phase functionals, HOKKAIDO MATHEMATICAL JOURNAL, 52(2), 331-352, 202306
  13. ★, Sobolev's Inequality for Musielak-Orlicz-Sobolev Functions, RESULTS IN MATHEMATICS, 78(3), 202306
  14. ★, Hardy-Littlewood-Sobolev Theorem for Variable Riesz Potentials, RESULTS IN MATHEMATICS, 78(3), 202306
  15. Trudinger's Inequality on Musielak-Orlicz-Morrey Spaces Over Non-doubling Metric Measure Spaces, MEDITERRANEAN JOURNAL OF MATHEMATICS, 20(3), 202306
  16. Generalized fractional maximal operators on Musielak-Orlicz-Morrey spaces, POSITIVITY, 27(2), 202304
  17. RIESZ POTENTIALS AND SOBOLEV-TYPE INEQUALITIES IN ORLICZ-MORREY SPACES OF AN INTEGRAL FORM, CZECHOSLOVAK MATHEMATICAL JOURNAL, 73(1), 263-276, 202303
  18. Sobolev-Type Inequalities on Musielak-Orlicz-Morrey Spaces of an Integral Form, BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 46(1), 202301
  19. Trudinger-type inequalities in Musielak-Orlicz spaces, HOUSTON JOURNAL OF MATHEMATICS, 48, 479-497, 2022
  20. Sobolev and Trudinger inequalities in weighted Morrey spaces for double phase functionals, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 41(3-4), 439-466, 2022
  21. Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces, PORTUGALIAE MATHEMATICA, 79(3-4), 265-282, 2022
  22. Compact embeddings for Sobolev spaces of two variable exponents, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(12), 3009-3022, 20221202
  23. HARDY-SOBOLEV INEQUALITY IN HERZ SPACES, TOHOKU MATHEMATICAL JOURNAL, 74(2), 287-300, 2022
  24. GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT MORREY SPACES OF AN INTEGRAL FORM, ACTA MATHEMATICA HUNGARICA, 167(1), 201-214, 202206
  25. ★, Boundedness of fractional integral operators in Herz spaces on the hyperplane, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 45(14), 8631-8654, 20220930
  26. On Sobolev-type Inequalities on Morrey Spaces of an Integral Form, TAIWANESE JOURNAL OF MATHEMATICS, 26(4), 831-845, 202208
  27. HARDY AND SOBOLEV INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS ON THE UNIT BALL, MATHEMATICAL INEQUALITIES & APPLICATIONS, 25(2), 319-333, 202204
  28. Sobolev-type inequalities on variable exponent Morrey spaces of an integral form, RICERCHE DI MATEMATICA, 71(1), 189-204, 202206
  29. Maximal and Riesz Potential Operators in Double Phase Lorentz Spaces of Variable Exponents, MATHEMATICAL NOTES, 111(5-6), 729-735, 202206
  30. Sobolev's inequality in central Herz-Morrey-Musielak-Orlicz spaces over metric measure spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(5), 1154-1185, 20220504
  31. HARDY-SOBOLEV INEQUALITIES IN THE HALF-SPACE FOR DOUBLE PHASE FUNCTIONALS, ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 51(6), 2159-2169, 202112
  32. Hardy-Sobolev inequality for Sobolev functions in central Herz-Morrey spaces, MATHEMATISCHE NACHRICHTEN, 294(6), 1148-1159, 202106
  33. Nonhomogeneous central Morrey-type spaces in L-P(.) and weak estimates for the maximal and Riesz potential operators, KYOTO JOURNAL OF MATHEMATICS, 62(1), 133-150, 202204
  34. TRUDINGER-TYPE INEQUALITIES ON MUSIELAK-ORLICZ-MORREY SPACES OF AN INTEGRAL FORM, MATHEMATICA SCANDINAVICA, 128(1), 78-108, 2022
  35. CONTINUITY OF GENERALIZED RIESZ POTENTIALS FOR DOUBLE PHASE FUNCTIONALS WITH VARIABLE EXPONENTS, GLASNIK MATEMATICKI, 56(2), 329-341, 202112
  36. Hardy-Sobolev inequalities for Sobolev functions in central Herz-Morrey spaces on the unit ball, Ann. Fenn. Math., 46, 1031-1052, 20210802
  37. Sobolev embeddings in grand Morrey spaces, MATHEMATISCHE NACHRICHTEN, 294(12), 2367-2381, 202112
  38. BOUNDARY LIMITS OF MONOTONE SOBOLEV FUNCTIONS ON METRIC SPACES, OSAKA JOURNAL OF MATHEMATICS, 58(1), 135-147, 202101
  39. Weak Estimates for the Maximal and Riesz Potential Operators in Central Herz-Morrey Spaces on the Unit Ball, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 40(2), 183-207, 2021
  40. Boundedness of maximal operator, Hardy operator and Sobolev's inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces, HIROSHIMA MATHEMATICAL JOURNAL, 51(1), 13-55, 202103
  41. HERZ-MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING 1 AND DOUBLE PHASE FUNCTIONALS, NAGOYA MATHEMATICAL JOURNAL, 242, 1-34, 202106
  42. Trudinger's Inequality for Double Phase Functionals with Variable Exponents, CZECHOSLOVAK MATHEMATICAL JOURNAL, 71(2), 511-528, 202106
  43. SOBOLEV'S INEQUALITY FOR MUSIELAK-ORLICZ-MORREY SPACES OVER METRIC MEASURE SPACES, JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 110(3), 371-385, 202106
  44. Hardy-Sobolev inequalities in the unit ball for double phase functionals, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(1), 20210901
  45. Boundedness of fractional maximal operators for double phase functionals with variable exponents, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(1), 20210901
  46. THE DOUBLE OBSTACLE PROBLEM FORMUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES, TOHOKU MATHEMATICAL JOURNAL, 73(1), 119-136, 2021
  47. CONTINUITY OF GENERALIZED RIESZ POTENTIALS FOR DOUBLE PHASE FUNCTIONALS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 24(3), 715-723, 202107
  48. On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 64(1), 75-90, 202103
  49. ★, Fractional Maximal Operator on Musielak-Orlicz Spaces Over Unbounded Quasi-Metric Measure Spaces, RESULTS IN MATHEMATICS, 76(4), 202112
  50. BOUNDARY GROWTH OF SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 45, 279-292, 2020
  51. SOBOLEV'S THEOREM FOR DOUBLE PHASE FUNCTIONALS, MATHEMATICAL INEQUALITIES & APPLICATIONS, 23(1), 17-33, 202001
  52. ★, Generalized Riesz potentials of functions in Morrey spaces L-(1,L-phi;kappa)(G) over non-doubling measure spaces, FORUM MATHEMATICUM, 32(2), 339-359, 202003
  53. Sobolev's Inequality for Riesz Potentials of Functions in Musielak-Orlicz-Morrey Spaces Over Non-doubling Metric Measure Spaces, CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 63(2), 287-303, 202006
  54. Campanato-Morrey spaces for the double phase functionals with variable exponents, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 197, 202008
  55. Hardy and Sobolev inequalities in the half space, ACTA MATHEMATICA HUNGARICA, 161(1), 230-244, 202006
  56. WEAK ESTIMATES FOR THE MAXIMAL AND RIESZ POTENTIAL OPERATORS ON NON-HOMOGENEOUS CENTRAL MORREY TYPE SPACES IN L-1 OVER METRIC MEASURE SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 45, 1187-1207, 2020
  57. Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions, MATHEMATISCHE NACHRICHTEN, 293(6), 1156-1173, 202006
  58. Boundedness of the maximal and potential operators in Herz-Morrey type spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 65(9), 1575-1589, 20200901
  59. Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces, GEORGIAN MATHEMATICAL JOURNAL, 27(3), 433-439, 202009
  60. GAGLIARDO-NIRENBERG INEQUALITY FOR GENERALIZED RIESZ POTENTIALS OF FUNCTIONS IN MUSIELAK-ORLICZ SPACES OVER QUASI-METRIC MEASURE SPACES, COLLOQUIUM MATHEMATICUM, 161(1), 51-66, 2020
  61. BOUNDARY LIMITS OF MONOTONE SOBOLEV FUNCTIONS FOR DOUBLE PHASE FUNCTIONALS, OSAKA JOURNAL OF MATHEMATICS, 57(4), 819-826, 202010
  62. BOUNDEDNESS OF MAXIMAL OPERATORS ON HERZ SPACES WITH RADIAL VARIABLE EXPONENT, TOHOKU MATHEMATICAL JOURNAL, 72(3), 335-348, 2020
  63. Campanato-Morrey spaces for the double phase functionals, REVISTA MATEMATICA COMPLUTENSE, 33(3), 817-834
  64. Duality of central Herz-Morrey-Musielak-Orlicz spaces of variable exponents, COLLECTANEA MATHEMATICA, 70(1), 117-151, 201901
  65. ★, Sobolev's inequality for double phase functionals with variable exponents, FORUM MATHEMATICUM, 31(2), 517-527, 201903
  66. OBSTACLE PROBLEM FOR MUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES, TOHOKU MATHEMATICAL JOURNAL, 71(1), 53-68, 2019
  67. BOUNDARY GROWTH OF GENERALIZED RIESZ POTENTIALS ON THE UNIT BALL IN THE VARIABLE SETTINGS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 44, 125-140, 2019
  68. Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L-1 Over Metric Measure Spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 69(1), 207-223, 201903
  69. Lindelof theorems for monotone Sobolev functions in Orlicz spaces on uniform domains, MATHEMATISCHE NACHRICHTEN, 292(4), 793-804, 201904
  70. OPTIMAL ESTIMATES FOR THE FRACTIONAL HARDY OPERATOR ON VARIABLE EXPONENT LEBESGUE SPACES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 22(2), 445-462, 201904
  71. ROUNDEDNESS OF GENERALIZED RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES L-(1,L-phi:kappa) (G) OVER NON-DOUBLING MEASURE SPACES, MATHEMATICAL INEQUALITIES & APPLICATIONS, 22(2), 577-599, 201904
  72. MAXIMAL OPERATOR ON ORLICZ SPACES OF TWO VARIABLE EXPONENTS OVER UNBOUNDED QUASI-METRIC MEASURE SPACES, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147(7), 2877-2885, 201907
  73. Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 64(9), 1437-1456, 20190902
  74. Sobolev inequalities for Musielak-Orlicz spaces, MANUSCRIPTA MATHEMATICA, 155(1-2), 209-227, 201801
  75. SOBOLEV'S INEQUALITIES FOR HERZ-MORREY-ORLICZ SPACES ON THE HALF SPACE, MATHEMATICAL INEQUALITIES & APPLICATIONS, 21(2), 433-453, 201804
  76. A remark on modified Morrey spaces on metric measure spaces, HOKKAIDO MATHEMATICAL JOURNAL, 47(1), 1-15, 201802
  77. GROWTH PROPERTIES OF POTENTIALS IN CENTRAL MORREY-ORLICZ SPACES ON THE UNIT BALL, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 21-46, 2018
  78. VARIABLE EXPONENT WEIGHTED NORM INEQUALITY FOR GENERALIZED RIESZ POTENTIALS, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 43(1), 563-577, 2018
  79. ★, Boundary Behavior of Monotone Sobolev Functions in Orlicz Spaces on John Domains in a Metric Space, JOURNAL OF GEOMETRIC ANALYSIS, 28(2), 1233-1244, 201804
  80. Generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces, GEORGIAN MATHEMATICAL JOURNAL, 25(2), 303-311, 201806
  81. Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball, COLLECTANEA MATHEMATICA, 69(3), 377-394, 201809
  82. Maximal and Riesz Potential Operators on Musielak-Orlicz Spaces Over Metric Measure Spaces, INTEGRAL EQUATIONS AND OPERATOR THEORY, 90(6), 201812
  83. Sobolev's inequality for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces, MATHEMATISCHE NACHRICHTEN, 291(10), 1547-1562, 201807
  84. Trudinger's inequality and continuity for Riesz potential of functions in Orlicz spaces of two variable exponents over nondoubling measure spaces, KYOTO JOURNAL OF MATHEMATICS, 57(1), 79-96, 201704
  85. Boundary limits of monotone Sobolev functions in Musielak-Orlicz spaces on uniform domains in a metric space, KYOTO JOURNAL OF MATHEMATICS, 57(1), 147-164, 201704
  86. Boundedness of the Generalized Fractional Integral Operators on Generalized Morrey Spaces over Metric Measure Spaces, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 36(2), 159-190, 2017
  87. Generalized fractional integral operators over non-doubling metric measure spaces, INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 28(7), 534-546, 201707
  88. Growth properties near the origin for generalized Riesz potentials, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 454(1), 285-302, 2017
  89. Duality of Non-Homogeneous Central Herz-Morrey-Musielak-Orlicz Spaces, POTENTIAL ANALYSIS, 47(4), 447-460, 2017
  90. BOUNDEDNESS OF THE MAXIMAL OPERATOR ON MUSIELAK-ORLICZ-MORREY SPACES, TOHOKU MATHEMATICAL JOURNAL, 69(4), 483-495, 2017
  91. Growth properties for Riesz potentials of functions in weighted variable Lp(.) spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 162, 49-75, 201710
  92. SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN Lp(.) OVER NONDOUBLING MEASURE SPACES, BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 93(1), 128-136, 2016
  93. Boundedness of Generalized Fractional Integral Operators From the Morrey Space L-1,L-phi(X; mu) to the Campanato Space L-1,L-psi(X; mu) Over Non-doubling Measure Spaces, AZERBAIJAN JOURNAL OF MATHEMATICS, 6(2), 117-127, 201607
  94. SOME NORM INEQUALITIES IN MUSIELAK-ORLICZ SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 41(2), 721-744, 2016
  95. Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 66(2), 371-394, 2016
  96. Trudinger's inequality and continuity for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces, KYOTO JOURNAL OF MATHEMATICS, 56(3), 633-653, 201609
  97. Boundedness of Maximal Operators and Sobolev's Inequality on Non-Homogeneous Central Musielak-Orlicz-Morrey Spaces, MEDITERRANEAN JOURNAL OF MATHEMATICS, 13(5), 3341-3357, 201610
  98. Growth properties of Musielak-Orlicz integral means for Riesz potentials, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 112, 69-83, 201501
  99. Boundary limits of monotone Sobolev functions with variable exponent on uniform domains in a metric space, REVISTA MATEMATICA COMPLUTENSE, 28(1), 31-48, 201501
  100. SOBOLEV AND TRUDINGER TYPE INEQUALITIES ON GRAND MUSIELAK-ORLICZ-MORREY SPACES, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 40(1), 403-426, 2015
  101. Musielak-Orlicz-Sobolev spaces on metric measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 65(2), 435-474, 201506
  102. Weighted Morrey spaces of variable exponent and Riesz potentials, MATHEMATISCHE NACHRICHTEN, 288(8-9), 984-1002, 201506
  103. Boundedness of maximal operators and Sobolev's theorem for non-homogeneous central Morrey spaces of variable exponent, HOKKAIDO MATHEMATICAL JOURNAL, 44(2), 185-201, 201506
  104. Problem posing in the upper grades using computers, Mathematical Problem Posing, Springer-Verlag New York, 257-272, 2015
  105. Optimal estimates for the fractional Hardyoperator, STUDIA MATHEMATICA, 227(1), 1-19, 2015
  106. EXPONENTIAL INTEGRABILITY FOR LOGARITHMIC POTENTIALS OF FUNCTIONS IN GENERALIZED LEBESGUE SPACES L(log L)(q(.)) OVER NON-DOUBLING MEASURE SPACES, TAIWANESE JOURNAL OF MATHEMATICS, 19(6), 1795-1803, 201512
  107. Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 138(2), 225-235, 201403
  108. Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 106, 1-17, 201409
  109. Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 64(1), 209-228, 201403
  110. Sobolev embeddings for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces over non-doubling measure spaces, INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 25(12), 976-991, 20141202
  111. Hardy's inequality in Musielak-Orlicz-Sobolev spaces, HIROSHIMA MATHEMATICAL JOURNAL, 44(2), 139-155, 201407
  112. SOBOLEV EMBEDDINGS FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES L-1,L-nu,L- beta 1,L-beta 2(R-n), MATHEMATICAL INEQUALITIES & APPLICATIONS, 17(4), 1399-1414, 201410
  113. Trudinger's Inequality and Continuity of Potentials on Musielak-Orlicz-Morrey Spaces, POTENTIAL ANALYSIS, 38(2), 515-535, 201302
  114. ★, Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces, BULLETIN DES SCIENCES MATHEMATIQUES, 137(1), 76-96, 2013
  115. On the Boundary Limits of Monotone Sobolev Functions in Variable Exponent Orlicz Spaces, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 29(3), 461-470, 201303
  116. Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces L-(1,L-phi)(G) over Nondoubling Measure Spaces, JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013
  117. Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65(2), 633-670, 201304
  118. Hardy Averaging Operator on Generalized Banach Function Spaces and Duality, ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 32(2), 233-255, 2013
  119. ★, Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents, COLLECTANEA MATHEMATICA, 64(3), 313-350, 201309
  120. Approximate identities and Young type inequalities in Musielak-Orlicz spaces, CZECHOSLOVAK MATHEMATICAL JOURNAL, 63(4), 933-948, 201312
  121. Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponentattaining the value $1$ over non-doubling measure spaces, Journal of Inequalities and Applications, 2013:12, 20130101
  122. Mean continuity for potentials of functions in Musielak-Orlicz spaces, RIMS K\^{o}ky\^{u}roku Bessatsu., B43, 81-100, 20130901
  123. Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces, JOURNAL OF INEQUALITIES AND APPLICATIONS, 1-19, 2013
  124. LINDELOF THEOREMS FOR MONOTONE SOBOLEV FUNCTIONS IN ORLICZ SPACES, ILLINOIS JOURNAL OF MATHEMATICS, 57(4), 1025-1033, 2013
  125. Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in R-n, REVISTA MATEMATICA COMPLUTENSE, 25(2), 413-434, 201207
  126. A trace inequality of Riesz potentials in variable exponent Orlicz spaces, MATHEMATISCHE NACHRICHTEN, 285(11-12), 1466-1485, 201208
  127. Weighted Sobolev inequality in Musielak-Orlicz space, J. Math. Anal. Appl., 388, 86-97, 20120101
  128. Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Orlicz-Musielak spaces, Arch. Math., 98, 253-263, 20120301
  129. Weighted Sobolev inequality in Musielak-Orlicz space, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 388(1), 86-97, 20120401
  130. Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces, ARCHIV DER MATHEMATIK, 98(3), 253-263, 201203
  131. EXPONENTIAL INTEGRABILITY OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS, ILLINOIS JOURNAL OF MATHEMATICS, 56(2), 507-520, 2012
  132. Iterated maximal functions in variable exponent Lebesgue spaces, MANUSCRIPTA MATHEMATICA, 135(3-4), 381-399, 201107
  133. Capacity for potentials of functions in Musielak-Orlicz spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 74(17), 6231-6243, 201112
  134. Hardy's inequality in Orlicz-Sobolev spaces of variable exponent, HOKKAIDO MATHEMATICAL JOURNAL, 40(2), 187-203, 201106
  135. Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 56(7-9), 671-695, 2011
  136. ORLICZ-SOBOLEV CAPACITY OF BALLS, ILLINOIS JOURNAL OF MATHEMATICS, 55(2), 543-553, 2011
  137. Sobolev's inequality for Riesz potentials in Orlicz-Musielak spaces, Proceedings of the International Symposium on Banach and Function Spaces III (Kitakyushu, Japan, 2009), 409-419, 2011
  138. Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent, BULLETIN DES SCIENCES MATHEMATIQUES, 134(1), 12-36, 2010
  139. Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 366(2), 391-417, 20100615
  140. COMPACT EMBEDDINGS FOR SOBOLEV SPACES OF VARIABLE EXPONENTS AND EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING THE p(x)-LAPLACIAN AND ITS CRITICAL EXPONENT, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 35(1), 115-130, 2010
  141. SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS, GLASGOW MATHEMATICAL JOURNAL, 52, 227-240, 201005
  142. Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62(3), 707-744, 201007
  143. Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form, MATHEMATISCHE NACHRICHTEN, 283(9), 1336-1352, 201009
  144. CONTINUITY PROPERTIES FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES OF VARIABLE EXPONENT, MATHEMATICAL INEQUALITIES & APPLICATIONS, 13(1), 99-122, 201001
  145. WEIGHTED ORLICZ-RIESZ CAPACITY OF BALLS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(12), 4291-4302, 201012
  146. Variable exponent spaces on metric measure spaces, More progresses in analysis (ISAAC-5, Catania, 2005, Begehr and Nicolosi (ed.)), 107-121, 2009
  147. Continuity properties of Riesz potentials of Orlicz functions, Tohoku Mathematical Journal, 61(2), 225-240, 20090601
  148. CONTINUITY PROPERTIES OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS, TOHOKU MATHEMATICAL JOURNAL, 61(2), 225-240, 200906
  149. SOBOLEV'S INEQUALITY FOR RIESZ POTENTIALS OF FUNCTIONS IN NON-DOUBLING MORREY SPACES, OSAKA JOURNAL OF MATHEMATICS, 46(1), 255-271, 200903
  150. ★, MAXIMAL FUNCTIONS IN VARIABLE EXPONENT SPACES: LIMITING CASES OF THE EXPONENT, ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 34(2), 503-522, 2009
  151. Integrability of maximal functions in Orlicz spaces of variable exponent, 京都大学数理解析研究所講究録, 1669, 37-51, 2009
  152. Sobolev's inequality for Orlicz-Sobolev spaces of variable exponents, 京都大学数理解析研究所講究録, 1669, 91-102, 2009
  153. An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{1,\nu,\beta}(G)$, Hiroshima Math. J., 38(3), 425-436, 20081101
  154. Lindel\"of theorems for monotone Sobolev functions with variable exponent, Proc. Japan Acad. Ser. A Math. Sci., 84, 25-28, 20080201
  155. Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 60(2), 583-602, 200804
  156. Lindelof theorems for monotone Sobolev functions with variable exponent, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 84(2), 25-28, 200802
  157. Integrability of maximal functions for generalized Lebesgue spaces with variable exponent, MATHEMATISCHE NACHRICHTEN, 281(3), 386-395, 2008
  158. Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(.)log L)q(.), JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 345(1), 70-85, 20080901
  159. Continuity properties and vanishing exponential integrability of Riesz potentials of Orlicz functions, 1553, 137-148, 2007
  160. Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes, ILLINOIS JOURNAL OF MATHEMATICS, 51(4), 1039-1060, 2007
  161. ★, Sobolev embeddings for Riesz potential space of variable exponent on metric spaces, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060601
  162. Sobolev embeddings for Riesz potential space of variable exponent, Math. Nachr., 279, 1463-1473, 20060401
  163. Sobolev embeddings for variable exponent Riesz potentials on metric spaces {\bf 31} (2006),, Ann. Acad. Sci. Fenn. Math., 31, 495-522, 20060401
  164. Sobolev embedding theorems for variable exponent Riesz potentials, 22, 21-30, 20060401
  165. Numerical computation of cross-coupled algebraic Riccati equations related to H(2)/H(infinity) control problem for singularly perturbed systems, INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 14(8), 697-717, 20040525
  166. Approach regions for modified Poisson integrals of boundary functions in Orlicz classes, Far East J. Math. Sci., 14, 137-153, 20040801
  167. Continuity of Sobolev functions of variable exponent on metric spaces, Proc.Japan Acad.Ser.A, 80(6), 96-99, 20040601
  168. Sobolev embeddings for Riesz potential space of variable exponent, 109-115, 20040801
  169. Minimally fine limits at infinity for p-precise functions, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 56(1), 1-15, 200401
  170. Asymptotic Expansions of Solutions of Cross-coupled Algebraic Riccati Equations of Multimodeling Systems Related to Nash Games, Proceedings of the 3rd International DCDIS Conference on Engineering Applications and Computational Algorithms, 34-39, 20030501
  171. Growth properties for modified Poisson integrals in a half space, Pacific J. Math., 212, 333-346, 20031201
  172. On semi-fine limits at infinity for Riesz potentials and monotone BLD functions, POTENTIAL ANALYSIS, 19(4), 365-381, 200312
  173. Growth properties for modified Poisson integrals in a half space, PACIFIC JOURNAL OF MATHEMATICS, 212(2), 333-346, 200312
  174. Asymptotic expansions and a new numerical algorithm of the algebraic Riccati equation for multiparameter singularly perturbed systems, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 267(1), 209-234, 20020301
  175. Near-Optimal Control of Linear Multiparameter Singularly Perturbed Systems, IEEE Transactions on Automatic Control, 47(12), 2051-2057, 20021201
  176. Numerical Algorithm for Solving Cross-Coupled Algebraic Riccati Equations Related to Nash Games of Multimodeling Systems, Proceedings of the 41th IEEE Conference on Decision and Control (CDC), 4167-4172, 20021201
  177. Lindel\"{o}f type theorems for monotone Sobolev functions on half spaces, 1293, 18-26, 20021101
  178. Riesz decomposition and limits at infinity for $p$-precise on a half space, 1293, 98-109, 20021101
  179. Growth properties for modified Poisson integrals in a half space, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 110-123, 20021201
  180. Continuity and differentiability for weighted Sobolev spaces, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 130(10), 2985-2994, 2002
  181. Growth properties of hyperplane integrals of Sobolev functions in a half space, Osaka J. Math., 38, 759-773, 20011201
  182. Minimally fine limits at infinity for $p$-precice functions, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 61-77, 20011001
  183. Growth properties of spherical means for monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math., 25, 457-465, 20000401
  184. Monotone BLD functions and fine properties, Proceedings of the Workshop on Real and Complex Analysis= Hiroshima University, 50-66, 20000401
  185. Hyperplane integrals of BLD and monotone BLD functions, 1116, 51-68, 19990401
  186. Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math., 24, 45-60, 19990401
  187. Exponential integrability for Riesz potentials of functions in Orlicz classes, Hiroshima Math. J., 28, 19980401
  188. Continuity properties and exponential integrability for Riesz potentials of functions in Orlicz classes, 1016, 94-111, 19970401
  189. H\"{o}lder continuity of Riesz potentials of functions in Orlicz classes, 161-172, 19960401
  190. Taylor expansion of Riesz potentials, Hiroshima Math. J., 25, 595-621, 19951101
  191. Integrability of maximal functions for generalized Lebesgue spaces $L^{p(\cdot)}(\log L)^{q(\cdot)}$, Proceedings of the Conference on Potential Theory and Stochastics in Albac: Aurel Cornea Memorial Volume, 193-202, 2009

Invited Lecture, Oral Presentation, Poster Presentation

  1. Boundary behavior of monotone Sobolev functions on John domains, 2017/10/07, With Invitation, Japanese
  2. Sobolev inequalities for Musielak-Orlicz spaces, 下村哲, Nonstandard growth phenomena 2017, 2017/08/31, Without Invitation, Japanese
  3. Sobolev inequalities for variable exponent Orlicz spaces, 2010/08/02, With Invitation, Japanese

External Funds

Acceptance Results of Competitive Funds

  1. KAKENHI, 2015, 2017
  2. KAKENHI, 2012, 2014
  3. KAKENHI, Study on the problem posing activity in the mathematics education, 2009, 2011
  4. KAKENHI, Potential theoretic study of elliptic partial differential equations, 2009, 2011
  5. KAKENHI, Research on potential problems from various aspects, 2008, 2012
  6. KAKENHI, Potential theoretical research for nonlinear partial differential equations, 2008, 2011
  7. KAKENHI, Potential theoretic study of Sobolev functions, 2007, 2008
  8. KAKENHI, Study on the design of broadening mathematical thinking in the mathematics education, 2006, 2008
  9. KAKENHI, Analyses of function spaces of solutions of a parabolic equation and operators on these spaces, 2006, 2008
  10. KAKENHI, 2005, 2007
  11. KAKENHI, New development of geometric function theory focused on conformal invariants, 2005, 2008
  12. KAKENHI, 2004, 2005
  13. KAKENHI, Potential Analysis for Sobolev functions, 2002, 2005
  14. KAKENHI, Study of integral operators on function spaces., 2002, 2003
  15. KAKENHI, Potential the Oretic study on quasi-regular mappings, 1998, 1999
  16. KAKENHI(Grant-in-Aid for Scientific Research (C)), 2018, 2020

Social Activities

Organizing Academic Conferences, etc.

  1. Nonstandard growth phenomena 2017, 2017/, 2017/
  2. 調和解析とポテンシャル論, 2015/, 2015/
  3. The 19th International Conference on Finite or Infinite Dimensional complex Analysis and Applications, 2011/
  4. International Workshop on Potential Theory in Hokkaido 2009, 2009/, 2009/
  5. FSDONA (Function Spaces, Differential Operators and Nonlinear Analysis)-Workshop, 2008/, 2008/
  6. 2007/, 2007/